maths

Research notes, computational certificates, and reproducible manuscripts. Maintained by Angus Muffatti. All results are AI-assisted and carry explicit disclosures; all claims are unverified until independently audited.

Provenance. This repository builds on attributed third-party work: the DGG/Goemans flow counterexample is due to Dmitry Rybin (with GPT-5.6 Pro), and the Jacobian-conjecture starting map is due to Levent Alpöge, Akhil Mathew, and Claude Fable 5. See ATTRIBUTIONS.md for citations and PROVENANCE_AUDIT.md for the exact boundary between that work and this repository's own results.

Results (one folder per independent result)

• chairman-counterexample/ — counterexample to the machine-dependent weighted-chairman conjectures (Liu–Reis Conjectures 19 and 21), plus a quantitative strengthening: prefix discrepancy can be forced arbitrarily close to 7/6·D for the ½-split gadget (concrete 49×72 instance > 9/8), improved to (4−2√2)·D − ε ≈ 1.1716·D by freeing the detector split (exact witness 239/204). Six independent verifiers (exact-rational and MILP). Author: Angus Muffatti.
• detector-chains/ — a Lambert-W lower bound for machine-dependent chairman assignment (working draft): deepening the companion paper's detector to a chain of length k gives the closed form τ(k) and the limit κ ≥ 1 + W(1/e) ≈ 1.2785, with exact certificates to depth 40 (deepest instance 1.272743) and exhaustive, solver-free verification of the block-game section. Author: Angus Muffatti.
• subtree-shuffling-counterexample/ — explicit fixed-parameter obstruction to the subtree-shuffling conjecture at (d,p) = (7,15) for all k = 3m, via a weighted Horner suspension of the Alpöge map (attributed) and an exact Lagrange-inversion certificate. Author: Angus Muffatti.
• planar-cost-lower-bound/ — corollaries of Rybin's counterexample (Morell–Skutella convex-decomposition failure) and the planar 9/8 lower bound for cost-preserving unsplittable flow, giving α_planar ∈ [9/8, 2]. Base instance due to Rybin (attributed). Author of the note: Angus Muffatti.

Archived combined packages

• 2026-rounding-counterexamples/ and 2026-dgg-and-chairman-counterexamples/ — earlier combined packages bundling Rybin's DGG counterexample with the chairman result. Superseded by the per-result folders above; retained for the record with attribution notes intact.

Every result folder carries its own README, verification instructions, data, and manuscript source; manuscripts build with latexmk -pdf.